Find the Derivative - d/dx (x^4)/16

Problem

d()/d(x)(x4)/16

Solution

1. Identify the constant factor in the expression, which is 1/16

2. Apply the constant multiple rule of differentiation to move the constant outside the derivative.

d()/d(x)(x4)/16=1/16d(x4)/d(x)

3. Apply the power rule for differentiation, which states that d(xn)/d(x)=n*x(n−1)

d(x4)/d(x)=4*x3

4. Substitute the result back into the expression and simplify the fraction.

1/16⋅4*x3=(4*x3)/16

5. Simplify the coefficient by dividing both the numerator and denominator by 4.

(4*x3)/16=(x3)/4

Final Answer

d()/d(x)(x4)/16=(x3)/4

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